You can make PRNGs based on approximations to (disjunctive) irrational numbers, and the irrationality of the number being approximated is important to its quali

You can make PRNGs based on approximations to (disjunctive) irrational numbers, and the irrationality of the number being approximated is important to its quality. I'm not aware of any widespread real-world PRNGs constructed this way because they're less efficient than traditional PRNGs. It's mostly a mathematical trick to be used in proofs and thought experiments. I suspect they're referring to the more common practice of taking the first N digits of a well known number like Pi or e that happens to be irrational as a magic constant of known provenance. 1245678 is another common one though, which obviously isn't irrational.